Extroverted Intuition (Ne): Meowth is always bursting with ideas: practical, impractical, and everywhere in between. He always has some new scheme to catch Pikachu or another valuable Pokemon. Some of these are more outrageous than others, and all of them tend to fail. Meowth seldom or never revisits old ideas for catching Pikachu, preferring to devise new ones instead. Especially in the Advanced Generation series (the Hoenn and Battle Frontier story arcs), he comes up with elaborate (and nonsensical) "Boss Fantasies," in which he will dream up some fanciful way that Giovanni will be able to use a Pokemon that "Meowth and friends" will steal for their beloved boss.
Introverted Thinking (Ti): Meowth is an avid problem-solver who thinks outside the box. Trying to impress a female Meowth, he learned to walk and talk like a human, a feat that few Pokemon have ever managed to accomplish. To impress a human crush later on, he devises an elaborate and creative plan to get her Paras to evolve into a Parasect. He looks for means outside of conventional strategies to win battles when outmatched. He also has a philosophical streak, delving into life's questions when an inspiration comes to him.
Extroverted Feeling (Fe): Meowth wears his heart on his sleeve; he is openly excited when discussing a new plan or idea he has. He has a certain charisma about him, and can very often get others to believe him; he even once fooled Ash, Iris, and Cilan into believing that he had gotten himself expelled from Team Rocket. He is very hurt when he sees that Giovanni has a new favorite cat, and much of his motivation immediately following this stems from his desire for redemption in Giovanni's eyes. Meowth also has a tender, caring side; when Jessie and James stole a Pokemon egg from Ash, Misty, and Brock, Meowth spent most of his time nursing it until it hatched.
Introverted Sensing (Si): Meowth carries various memories around from his past, which he revisits from time to time. They are usually centered around unrequited romantic interests or the hard time he had while living on the streets. However, on the whole, Meowth prefers not to dwell on the memories that are so painful to him. He would rather look forward to his next attempted theft with the friends who are his only "family" now.
Note: At one time, I was toying with the idea of Meowth as an ENFJ. However, Meowth does not possess the focus that is characteristic of Ni; he is too scatterbrained and prolific in his insights. Another mistyping I've run into for Meowth is ENTJ; this poses another problem in addition to the one already mentioned. Meowth has no desire to dominate his environment (which he would have in spades with dominant Te), and he is never really in a power struggle with Jessie; we see instead that Meowth is an innovator who is the creative force of his squad, content to let Jessie take care of the nuts and bolts of leadership.